All about inheritance, succession, and descent, in various languages and cultures, nat- and con-.

1. Suppose the only primary kinterms are: Father, Mother, Son, and Daughter.
And suppose all other kinterms are sensitive to the sexes of ALTER and of all the connecting relatives (but not of EGO),
and also are sensitive to the relative ages (who's younger and who's older) of everybody in the chain.
Then there might be FACT(2+1)*(2^2) = 6*4 = 24 secondary kinterms;
and FACT(3+1)*(2^3) = 24*8 = 192 tertiary kinterms;
and FACT(4+1)*(2^4) = 120*16 = 1920 quaternary kinterms.
I believe it's reasonable for a language to have all 24 of those secondary kinterms as one-word kinterms, and there might very well be -- probably are -- some natlangs that have all 24 of them as one-word terms;
and that it's reasonable for a language to have all 192 of those ternary kinterms as one-word kinterms, and possibly there is a natlang that has all 192 of them.
But I don't think any natural language has 1000 or more one-word kinterms; and it's probably not reasonable or "naturalistic" or "realistic" for a conlang to have that many one-word kinterms.
(If the conspeakers' species were non-human, or significantly modified humans, it might be reasonable; or not.)
So I'm betting most quaternary and/or quinary and/or >=6th-degree kinterms, if there are any, are phrasal, and/or considerably less information-dense than telling the sexes and relative ages of every connecting relative.

The secondary kinterms would have the following meanings:

Parents' parents

Grandfathers

Father's father

Mother's father

Grandmothers

Father's mother

Mother's mother

Parents' children (aka siblings)

Brothers

Agnate brothers

Father's son older than EGO

Father's son younger than EGO

Uterine brothers

Mother's son older than EGO

Mother's son younger than EGO

Sisters

Agnate sisters

Father's daughter older than EGO

Father's daughter younger than EGO

Uterine sisters

Mother's daughter older than EGO

Mother's daughter younger than EGO

Children's parents (aka spouses)

Husbands

Son's father

older than EGO

younger than EGO

Daughter's father

older than EGO

younger than EGO

Wives

Son's mother

older than EGO

younger than EGO

Daughter's mother

older than EGO

younger than EGO

Children's children

Grandsons

Son's son

Daughter's son

Granddaughters

Son's daughter

Daughter's daughter

I had intended to list all 192 ternary kin in a spoiler. Maybe I'll still do that, later.
I have no intention of listing all 1920 quaternary kin. If someone else did, I wouldn't want to read them all, so I don't think anyone else will want to read them all if I list them.

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2. Suppose the only primary kinterms are: Father, Mother, Brother, Sister, Husband, Wife, Son, and Daughter.
And suppose only men have Mothers or Sisters or Wives or Daughters (as primary kin), and only women have Fathers or Brothers or Husbands or Sons (as primary kin).
Perhaps there should be a term for "section-mate" or "skin-mate" that refers to a person the same sex as EGO who is related to everyone exactly the same way (that is, by exactly the same kinterm) EGO is related to them.
We might call it a degree-0 or 0-ary kinterm; it would refer to a male EGO's brothers (among other men) and to a female EGO's sisters (among other women).
Let's use the following abbreviations;
F for Father's or Father
M for Mother's or Mother
B for Brother's or Brother
Z for Sister's or Sister
H for Husband's or Husband
W for Wife's or Wife
S for Son's or Son
D for Daughter's or Daughter.
We'll also assume that the kinship system is classificatory in the following sense;
Any of EGO's skinmate's kin are related to EGO exactly the way they are to the skinmate;
and any skinmate of any of EGO's kin are related to EGO by the same kinterm as the first-mentioned kin.
So, for instance, if EGO is male,EGO call's EGO's skinmate's Mother "Mother"; and also calls EGO's Mother's skinmate "Mother"; andEGO call's EGO's skinmate's Sister "Sister"; and also calls EGO's Sister's skinmate "Sister"; andEGO call's EGO's skinmate's Wife "Wife"; and also calls EGO's Wife's skinmate "Wife"; andEGO call's EGO's skinmate's Daughter "Daughter"; and also calls EGO's Daughter's skinmate "Daughter".

Note that if EGO is male, EGO's MS (Mother's Son), ZB (Sister's Brother), WH (Wife's Husband), and DF (Daughter's Father), all refer either to EGO himself, or to one of EGO's skinmates.
Likewise if EGO is female, EGO's FD (Father's Daughter), BZ (Brother's Sister), HW (Husband's Wife), and SM (Son's Mother), all refer either to EGO herself, or to one of EGO's skinmates.
In general a Parent's Child or a Sibling's Sibling or a Spouse's Spouse, is a skinmate.
(A Child’s Parent is not a skinmate if they are opposite sex from EGO, but is a skinmate if the same sex.)

For a female EGO, the ten terms will be FM, FZ, FW=BM, BW, BD, HM, HZ, HD=SZ, SW, and SD.

Note that a male EGO's primary kin are all female; his secondary kin are all male; and his ternary kin are all female; etc.
and a female EGO's primary kin are all male; her secondary kin are all female; and her ternary kin are all male; etc.

Those for a female EGO I'll let the reader figure out. Or, maybe, I'll list them in a spoiler, later.

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Anyway, if we continue, there would be 116 4th-degree kinterms (58 for a male EGO and a male ALTER, and 58 for a female EGO and a female ALTER);
and 280 5th-degree kinterms (140 for male EGO and female ALTER, and 140 for female EGO and male ALTER).

Including "skinmate", that adds up to 473 kinterms of degree 5 or less.

But there'd be 676 sixth-degree kinterms. So I hypothesize that someone might be willing to have a conlang with one-word kinterms for the 473 kinterms of degree 5 or less, but no-one would find it reasonable or realistic or naturalistic to have a conlang-for-humans with one-word kinterms for relationships of degree 6 or more. (Or, at least, not any as detailed and precise as any of these.)
In other words, if the conspeakers want to describe a kinship relation of degree 6 or higher, they'll construct a phrase rather than having a single word for it. (Or be less precise.)

Last edited by eldin raigmore on 10 Apr 2018 07:36, edited 4 times in total.

Economic (etc.) reasons why someone might want to keep track of different children and siblings differently.

I am thinking of having Adpihi, at least at one point in its history, having a triple-descent or trilineal system.
Some inheritance will be patrilineal and some will be matrilineal; and succession will be along "the rope" (the Mundugumorgeun).
Also, some will go to the oldest child of the appropriate sex; some to the youngest child of the appropriate sex; and some will be split equally among the children of the appropriate sex.
Fixed assets, including real estate and furniture, will be inherited mother-to-daughter.
Portable goods, including specie, cash, livestock, and rolling stock, will be inherited father-to-son.
Intangible assets, including political office and religious office and magical power*, will be inherited by a child of the opposite sex.*(and intellectual property?)
(Perhaps some things will be inherited by the oldest child regardless of sex, some by the youngest child regardless of sex, and some split equally among all children regardless of sex.)

So it makes sense for every parent to keep track of:
* their oldest son;
* their youngest son;
* all their other sons;
* their oldest daughter;
* their youngest daughter;
* all their other daughters.

It makes sense for every man to keep track of:
* all of his father's sons who are older than he is,
** especially his father's oldest son;
* all of his father's sons who are younger than he is,
** especially his father's youngest son;
* all of his mother's sons who are older than he is,
** especially his mother's oldest son;
* all of his mother's sons who are younger than he is,
** especially his mother's youngest son.

He might have separate kinterms for each of these categories of brothers.

So far, I haven't mentioned a good reason for a man to keep track of his sisters.

It makes sense for every woman to keep track of:
* all of her mother's daughters who are older than she is,
** especially her mother's oldest daughter;
* all of her mother's daughters who are younger than she is,
** especially her mother's youngest daughter;
* all of her father's daughters who are older than she is,
** especially her father's oldest daughter;
* all of her father's daughters who are younger than she is,
** especially her father's youngest daughter.

She might have separate kinterms for each of these categories of sisters.

So far, I haven't mentioned a good reason for a woman to keep track of her brothers.

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I have read of a culture in which there are bride-prices.
The latest sister to get married just before a man marries, probably brings in enough as a bride-price, to allow his parents to pay a bride-price to arrange his own marriage.
Whichever sister brings in the bride-price that funds the bride-price for his own bride, he forms a lasting and special attachment to.

That might be a good reason for a man to keep track of, for instance, his youngest older sister. He might have a special kinterm for her.
She might also have a special kinterm for him; he might usually be her oldest younger brother.

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And there are, in some cultures, other good reasons for people to keep track of their oldest sibling (regardless of sex) and/or their youngest sibling (regardless of sex); they might have special kinterms for one or the other or both of these, different from the terms they use for their other siblings.

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Does any reader's conculture or conlang, or natculture or natlang, or any natculture or natlang you know about (or maybe even any conculture or conlang you know about), have similar motives, or even very different motives, for distinguishing certain offspring and/or certain siblings from others?

Last edited by eldin raigmore on 18 Mar 2017 23:57, edited 2 times in total.

Dravidian-style kinship, of which Proto-Dujajikiswə uses a matrilineal form, keeps track of whether a given kinsman is marriageable or not. This works by assigning a 0 or 1 to all members of a given sex (which sex gets the 1 determines whether the system is matrilineal or patrilineal), totaling up the value for all links in the familial chain, and seeing whether the result is odd or even. If odd, then the cousin is considered marriageable; if even, they're not considered cousins but siblings.

Wikipedia contributors wrote:Floyd Lounsbury discovered[1] a seventh, Dravidian, type of terminological system that had been conflated with Iroquois in Morgan’s typology of kin-term systems because both systems distinguish relatives by marriage from relatives by descent, although both are classificatory categories rather than based on biological descent. The basic idea is that of applying an even/odd distinction to relatives that takes into account the gender of every linking relative for ego’s kin relation to any given person. A MFBD(C), for example, is a mother’s father’s brother’s daughter’s child. If each female link (M,D) is assigned a 0 and each male (F,B) a 1, the number of 1s is either even or odd; in this case, even. However, variant criteria exist.[2][3][4] In a Dravidian system with a patrilineal modulo-2 counting system, marriage is prohibited with this relative, and a marriageable relative must be modulo-2 odd. There exists also a version of this logic with a matrilineal bias. Discoveries of systems that use modulo-2 logic, as in South Asia, Australia, and many other parts of the world, marked a major advance in the understanding of kinship terminologies that differ from kin relations and terminologies employed by Europeans.

The Dravidian kinship system involves selective cousinhood. One's father's brother's children and one's mother's sister's children are not cousins but brothers and sisters one step removed. They are considered consanguinous (pangali), and marriage with them is strictly forbidden as incestuous. However, one's father's sister's children and one's mother's brother's children are considered cousins and potential mates (muraicherugu). Marriages between such cousins are allowed and encouraged. There is a clear distinction between cross cousins, who are one's true cousins and parallel cousins, who are, in fact, siblings. Like Iroquois people, Dravidians refer to their father's sister as mother-in-law and their mother's brother as father-in-law.

I know this'll be the fourth time I've posted this, so I apologize for that, but the system in action in the conlang (Proto-Dujajikiswə also cares about whether the brother/sister is older or not; this is not strictly speaking a feature of a Dravidian-type system):

The Dravidian kinship system involves selective cousinhood. One's father's brother's children and one's mother's sister's children are not cousins but brothers and sisters one step removed. They are considered consanguinous (pangali), and marriage with them is strictly forbidden as incestuous.

These could be grandbrothers and grandsisters that I was positing in another thread.
Wow- neat!

I think the cut-off is likely to be between either 3rd-degree and 4th-degree relatives, or between 4th-degree and 5th-degree relatives.

I'm nearly certain that some language whose culture has the "Sudanese" style of kinship system, has "unanalyzable" one-word kinterms for all of the secondary relationships I've mentioned.
Even if that isn't the case, I'm pretty sure that, for any two of those relationships, some natlang uses two different unanalyzable (i.e. not transparently compound-words nor inflecting morphology) one-word kinterms to mean them (possibly among other meanings).

I don't know of any natlang that has a complete set of one-word "unanalyzable" 3rd-degree kinterms; but I wouldn't be surprised if it turns out, that for each two such relationships, some natural language uses two different unanalyzable one-word kinterms that distinguish those two 3rd-degree relationships from each other and also from any 2nd-degree or 1st-degree relationships. For instance, "child's spouse's father" has a one-word kinterm in Turkish; and I've read that "child's spouse's parent" is the most common 3rd-degree kinterm in terms of how many languages have one or more 3rd-degree one-word kinterm(s).
I doubt it is unrealistic or unnaturalistic or unreasonable for a conlang to have a complete set of one-word 3rd-degree kinterms of which most are unanalyzable or quasi-unanalyzable.

It seems much more likely that no natlang has a complete set of unanalyzable one-word 4th-degree kinterms.
But maybe one does; and maybe some conlang does.
Maybe some natlang -- or conlang -- has a few one-word 4th-degree kinterms, and fills out a complete set of 4th-degree kinterms by coining phrases for the rest of them. (Phrases such as "my mother's BWB" or "my uncle's brother-in-law" or "my MBW's brother", or "my wife's BWF" or my brother-in-law's father-in-law" or "my WBW's father".)

To me it seems unreasonable to expect any natlang or conlang to have too complete a set of overly-precise 5th-degree kinterms all be one-word kinterms, unless they're very agglutinative or synthetic or compound (or many of them are). I don't think a language's "primitive lexicon" would contain more than 3,000-5,000 highly-common terms nor more than 30,000-50,000 common terms (depending, of course, on what "term" means and how they are counted and what "common" and "highly common" mean). I don't think more than a quarter of their very common terms should be in a single semantic field. (And how many semantic fields should there be in their "primitive" lexicon? Around 600? Or many fewer?) I think more than 1000 (primitive or root or stem) terms in the same semantic field is unlikely; at least, unlikely for human languages. And I think a complete set of very-precise 5th-degree kinterms would probably contain more than 1000 terms. Odds are the conspeakers'd have to be sort-of-civilized to even know about more than a thousand relatives each! And they'd probably only know about most of them, not actually know them.

So I figure starting either with 4th-degree kin or with 5th-degree kin, most kinterms will be phrasal instead of one-word terms.

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Can anyone think of a good reason why anyone would want to keep track of all their 5th-degree or 6th-degree or 7th-degree kin?

There might be exogamy rules preventing them from marrying any 4th-degree kin or closer; so they might need kinterms for all their 4th-degree kin (like first-cousins-once-removed), even if most of them have to be phrasal instead of one-word terms.

5th-degree kin include 2nd-cousins, and 1st-cousins-twice-removed, for example. I know of no place where such kin are too close to marry in modern times.

eldin raigmore wrote:I would conjecture that 7th-degree-or-more-remote kin (third-cousins are 7th-degree kin) are marriageable to them in most societies (probably including most consocieties?).
Is there any reason why such kin should be considered too close to marry?
What does anyone else think?

maybe in societies with very very small founding populations? and-or when everyone has lifespans as long as the LOTR elves?

The founding population can't be too small, or everybody will be more closely related than 7th-degree.
If EGO and ALTER are more than 7 degrees apart, that means that any common ancestor they have must be at least four generations before either of them.
If, instead, one of EGO's four-generations-ago ancestors (one of EGO's 16 great^2-grandparents) is only three generations before ALTER (one of ALTER's 8 great-grandparents), they will be half-second-cousins-once-removed, a 7th-degree relationship.
Reciprocally if one of ALTER's great-great-grandparents is one of EGO's great-grandparents, they'll be 7th-degree kin.
OTOH even if they share all of their great-great-grandparents, they might only be 8th-degree kin; if, somehow, no great-grandparent of either were a full-sibling of any great-grandparent of the other (they'd have to each be a half-sibling of two different great-grandparents of the other instead).
They'll be within the 7th degree of kinship if:
either of them is an ancestor of the other 7 or fewer generations ago (7+0), or;
a parent of either of them is an ancestor of the other 6 or fewer generations ago (6+1), or;
a grandparent of either of them is an ancestor of the other 5 or fewer generations ago (5+2), or;
a great-grandparent of either of them is an ancestor of the other 4 or fewer generations ago (e.g. a great-great-grandparent) (4+3).

(BTW the 7+0 possibility and the 6+1 possibility, and I think even the 5+2 possibility, would require extra longevity, as you suggested.)

Assuming the founding population consisted of just 16 people (8 men and 8 women), I suppose it's possible that they pursue maximal out-crossing and avoid matings between any. two people who share an ancestor 3 or fewer generations before one of them and 4 or fewer generations before the other. Possible, but perhaps difficult in the face of chance events, and perhaps unlikely.
Thanks for the input! It made me think.

One reason why such a distant relative could be unmarriageable could be due to a clan system or something along those lines, rather than a biological basis. The Tirina system used in Sanmra works this way; your "family" can include some very distant relatives, but because they're legally considered part of your family/clan/house/whatever, they're ineligible to marry.

Setting aside step- or half-relatives, to them, "incest" means someone in the same family as you, someone from your birth family (e.g. if you previously married into another family), any direct ancestors, any direct descendants, and any siblings. So marrying a first cousin from a different family is not even worth commenting on, whereas marrying a distant relation who's part of your family would be completely taboo.

alynnidalar wrote:One reason why such a distant relative could be unmarriageable could be due to a clan system or something along those lines, rather than a biological basis. The Tirina system used in Sanmra works this way; your "family" can include some very distant relatives, but because they're legally considered part of your family/clan/house/whatever, they're ineligible to marry.
Setting aside step- or half-relatives, to them, "incest" means someone in the same family as you, someone from your birth family (e.g. if you previously married into another family), any direct ancestors, any direct descendants, and any siblings. So marrying a first cousin from a different family is not even worth commenting on, whereas marrying a distant relation who's part of your family would be completely taboo.

Yes, you're right.
For example one of my consocieties is divided into exhaustive and mutually exclusive patriclans (everyone inherits membership from their father),
and, independently, also is divided into exhaustive and mutually exclusive matriclans (everyone inherits membership from their mother).
No-one would marry anyone from the same patriclan, no matter how distantly related; nor from the same matriclan, again no matter how distantly related.
But a man and a woman who shared the same mother's mother's father, and also the same father's father's mother, but no other great-grandparents or closer ancestors, would probably be allowed to marry.
(They'd be double-half-second-cousins. That's two 6th-degree kinships; adding up to a 5th-degree kinship.)

Spoiler:

Actually, in that society, there is triple descent -- matriclans, patriclans, and "alterclans" (the Mundugumor geun or "rope", in which everyone inherits membership from the parent of the opposite sex).
And no-one can acquire a parent-in-law nor a child-in-law in any of the same clans as oneself -- neither the same patriclan nor the same matriclan nor the same "alterclan".
But the groom's mother and the bride's mother can share a patriclan;
and the groom's father and the bride's father can share a matriclan;
and the groom's father and the bride's mother can share an "alterclan".
The bride can't be from the same patriclan as the groom's mother, but may very well be from the same patriclan as the groom's father's mother.
Etc.

Edit: Spoiler Edited 2017/05/18 Thu May 18 12:36 to correct "patriclan" to "matriclan" and also to include a link to a Wikipedia entry about the Mundugumor rope.

Last edited by eldin raigmore on 18 May 2017 17:38, edited 3 times in total.

For specificity, consider only that or those kind or kinds of property or title which belong only to men, and pass from a man to his oldest son.

Men and boys might then have reasons to keep track of who, instead of themselves, is likeliest to inherit the property or succeed to the title.

For the man or boy who is the heir-apparent, this would be the heir-presumptive; for any other, it would be the heir-apparent.

(A property-holder or title-holder who is sonless would, I suppose, be keeping track of his oldest younger brother, or if that brother has deceased, his oldest younger brother's oldest son.
(However that's a complication I don't want to get distracted by yet.)

Non-heirs-apparent would also want to keep track of everyone ahead of them as opposed to everyone they're ahead of.

So, for a male propositus EGO, there might be separate terms for:
* father's father's oldest surviving son;
* any other of father's father's surviving sons older than father;
* father's father's oldest surviving son other than father, especially if younger than father;
* any other of father's father's surviving sons younger than father.

That is, four different terms for paternal uncle-by-blood (meaning full- and agnate half-brothers of father).

(DId I do that right? Or did I miss something?)

And if EGO(still male!) has no surviving brothers (that is, EGO's father has no other surviving sons than EGO himself), EGO might find useful separate terms for the following kinds of nephews;
* father's oldest other older-than-EGO son+'s oldest surviving son;
* any surviving son of any other of father's sons+ older than EGO;
* oldest surviving son of oldest younger-than-EGO father's son+ who has a surviving son;
* any other surviving son of any younger-than-EGO father's son+.

+(pre-deceased)

(Seeing and hearing how complicated that looks and sounds, I wonder if I ought to postpone it a while too. Or maybe some reader can simplify it for me/us?)

In general, a grandson (a son's son) of a titleholder, when considering his cousins, might want to keep track of the following:

Is ALTER male?

(If 1), is ALTEREGO's cousin because their father's father is also EGO's father's father?

(And, that's also getting complex, isn't it? Are we already in the territory where we need either phrasal terms, or compound-word terms, or polyagglutinative terms, or some such?)

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We could swap "old" with "young" (and "older" with "younger" and "oldest" with "youngest").
And we could substitute "female" for "male" (and "mother" for "father" and "daughter" for "son" and "sister" for "brother" and "uterine" for "agnate" and "aunt" for "uncle" and "niece" for "nephew").

For property and/or title which goes to the oldest or youngest surviving child of the opposite sex, something could be worked out, which would be no more complicated (also no simpler!) if presented diagrammatically; but because English doesn't have simple terms for opposite-sex-parent and opposite-sex-child, it might be a lot wordier to describe.

Probably the easiest subsystems to come up with terms for, would be the male primogeniture and male ultimogeniture terms for a male EGO's uncles (father's father's sons), and the female "primogeniture"(? correct term?) and "ultimogeniture"(? correct term?) for a female EGO's aunts (mother's mother's daughters).

Other than my own (possibly temporary) mental limitations, I don't see why the reciprocal relationships are any harder.
But, so far, they appear to have been more difficult; at least for me.

Again supposing that "primary kin" means only parent and child;
and that kinterms encode the sex of ALTER and of every connecting relative except EGO (if there are any);
and that they encode the relative ages of everyone in the chain;
and that they also encode the life status (surviving or deceased) of each connecting relative other than EGO and ALTER;
the number of distinguished nth-degree kintypes will be
(2^n)*(2^(n-1))*FACTORIAL(n+1).
So there'd be 4 1st-degree kintypes (mother, father, daughter, son);
and 4*2*(3!)=8*6=48 2nd-degree kintypes;
and 8*4*(4!)=32*24=768 3rd-degree kintypes;
and 16*8*(5!)=128*120=15,360 4th-degree kintypes.

I don't think any reasonably realistic/naturalistic human language will have distinct unanalyzable one-word terms for all 15,360 4th-degree kintypes if they are that precise.

Listing all 48 2nd-degree kintypes, with this added bit of precision, may be a bit much for some readers, so I'll put it in the following spoiler.

Spoiler:

parents' parents (i.e. grandparents)

mother of living mother

mother of deceased mother

mother of living father

mother of deceased father

father of living mother

father of deceased mother

father of living father

father of deceased father

parents' children (i.e. half-siblings etc.)

(half-)siblings older than EGO

(older) daughter of living mother

(older) daughter of deceased mother

(older) daughter of living father

(older) daughter of deceased father

(older) son of living mother

(older) son of deceased mother

(older) son of living father

(older) son of deceased father

(half-)siblings younger than EGO

(younger) daughter of living mother

(younger) daughter of deceased mother

(younger) daughter of living father

(younger) daughter of deceased father

(younger) son of living mother

(younger) son of deceased mother

(younger) son of living father

(younger) son of deceased father

children's parents (i.e. spouses etc.)

mother of living daughter

"wife" older than EGO

"wife" younger than EGO

mother of deceased daughter

"wife" older than EGO

"wife" younger than EGO

mother of living son

"wife" older than EGO

"wife" younger than EGO

mother of deceased son

"wife" older than EGO

"wife" younger than EGO

father of living daughter

"husband" older than EGO

"husband" younger than EGO

father of deceased daughter

"husband" older than EGO

"husband" younger than EGO

faher of living son

"husband" older than EGO

"husband" younger than EGO

father of deceased son

"husband" older than EGO

"husband" younger than EGO

children's children (i.e. grandchildren)

daughter of living daughter

daughter of deceased daughter

daughter of living son

daughter of deceased son

son of living daughter

son of deceased daughter

son of living fatherson

son of deceased fatherson

The relationship between grandparent and grandchild may change if the (grandchild's parent)/(grandparent's child) dies;
the grandparent may have to become the grandchild's "back-up parent".

The relationship between two children of the same parent may change if their parent dies.
Maybe the older sibling has to become the younger sibling's "back-up parent".
Or, maybe, one of them (e.g. the male one or the older one) inherits some property or succeeds to some position (e.g. "head of the family" or "head of the household") and the other does not.

The relationship between two parents of the same child often changes if/when that child dies.
If they were married this frequently marks the end of the marriage; if they were betrothed this frequently marks the end of the betrothal.
If they were divorced, this frequently marks the end of some continuing relationship (whether amicable or acrimonious) they had, or some continuing obligation they had, while their shared child was alive.
(Sometimes, some of these obligations end when the child reaches the age of majority, rather than, or as well as, when the child dies.)

I have read that there are natlangs whose kinterm system do depend on the life-status of the connecting relative(s). I can't remember which ones; I can't even remember where I read it.

I don't think 768 third-degree kinterms are an unreasonable number for a human language; neither a natlang nor a conlang.
But I do think it's an unreasonable amount of text to post to a phpBBoard. It might be too much to put in a single post; if so, it wouldn't really help to put it in a spoiler.

However, I do wonder how useful it would be for a third-degree kinterm to reflect all four combinations of possible life-status for both of the intervening relatives.
Maybe it would be likelier that there's one term for "they're both still alive" vs one term for "at least one of them has passed away";
or one term for "they've both parted this vale of tears" vs one term for "at least one of them yet lives".

This is similar to my previously-expressed "I wonder ..." concerning how useful it would be to have one term for "spouse older than EGO" and a different term for "spouse younger than EGO".

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Speaking of things which have been useful to me;

On the (now unreachable -- temporarily so, I hope) conworlds.com/cwbb, I and a few of my co-posters found it useful to distinguish relationships as follows:
* ALTER is EGO's parent of the same sex as EGO
* ALTER is EGO's parent of a different sex from EGO
* ALTER is EGO's child of the same sex as EGO
* ALTER is EGO's child of a different sex from EGO

We were frequently discussing species with three sexes. (And briefly and infrequently discussing species with four sexes, once touching lightly on species with five sexes, and mentioning those with six or more only to say we'd say no more about them.)
That's why I said "different sex from" rather than saying "opposite sex from".
Grandparent, grandchild, and part-sibling relationships, were called by five different terms, depending on which of the following were true:

EGO and ALTER and the connecting relative were all the same sex.

EGO and ALTER were the same sex, but the connecting relative was a different sex.

EGO and the connecting relative were the same sex, but ALTER was a different sex.

ALTER and the connecting relative were the same sex, but EGO was a different sex.

EGO and ALTER and the connecting relative were all three different sexes.

(We also briefly considered great-grandparent and great-grandchild relationships in this way.
(But I don't remember talking about any fourth-or-further-degree relationships, and if we talked about other 3rd-degree relations besides great-grands, we didn't talk about them in this same-sex-vs-different-sex way.)

I remember reading of a natlang with four terms for "sibling";
* sibling is same sex as EGO and older than EGO;
* sibling is same sex as EGO and younger than EGO;
* sibling is opposite sex from EGO and older than EGO;
* sibling is opposite sex from EGO and younger than EGO.

How likely, and/or naturalistic, and/or realistic, and/or reasonable, and/or useful, do kinterminologies based on same-sex-vs-opposite-sex rather than male-relative-vs-female-relative, seem to the readers of this thread?
If you have actual logical reasons, or evidence, or statements from academic/professional journals or textbooks or whatever, to bring to bear on these questions, could you let me/us know about them? Their gist, and where to find them? URLs are great, but so are publishing information of the sort one would put in a citation.